The atmospheric pass of the optimal heating-rate constrained aeroassisted orbital plane-change problem is considered. The problem formulation includes the thrust magnitude as a control variable. The junction conditions are the optimality conditions that must be satisfied by every pair of adjoining subarcs of the optimal trajectory. An analysis of these junction conditions shows that a number of prior assumptions on concatenating optimal subarcs must be revised. This is because the Hamiltonian of the problem is no longer regular due to the inclusion of thrust magnitude as a control variable. Necessary conditions for jump discontinuities in the angle of attack and thrust control are derived. We show that these necessary conditions permit a nontangential entry. Our conditions also show that a number of extremals hitherto not considered in the literature should be included in the construction of the switching structure. In addition, a number of new junction conditions are derived that may be used by numerical analysts to validate their codes. One interesting consequence of our analysis is a demonstration of the dual relationship between singular points and touch points.
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics